Demonstration of Artificial Spin States Using Sub-Harmonic Injection Locking in AlN-on-Si Length-Extensional Mode MEMS Self-Sustaining Oscillator

We report on phase state control via injection locking phenomena in piezoelectric microelectromechanical systems (MEMS) based self-sustaining oscillators. By applying a sub-harmonic injection locking (SHIL) signal on piezoelectric AlN-on-Si (AlN/Si) length-extensional (LE) mode MEMS feedback oscillator, we create bistable phase states, which is the first demonstration of spin-mimicking up and down states of an Ising model using MEMS-based self-sustaining oscillators. In this work, we first characterize the oscillator performance, e.g., phase noise and frequency stability (Allan deviation) to examine the computational capabilities of these MEMS oscillators for Ising machines. Then we explore the probabilities of getting bistable phase states with varying injection locking voltage. This bistability in phase space can be utilized to build large-scale Ising machines using coupling between MEMS oscillators. Furthermore, it enables the utilization of the MEMS oscillators as binary logic latches, where the logic value can be encoded within the phase of oscillation. Finally, we have numerically solved a 4-node Max-Cut problem with various binary weight configurations using the complex Ginzburg-Landau (CGL) model for coupled self-sustaining MEMS oscillators.